Even if there are tools to convert between classic ASP and ASP.NET, they're not going to generate very good results: the two environments are just too fundamentally different. A quick Google turns up a few results, mostly of the "we'll have our guys in India do it" variety.
My advice would be not to touch your existing ASP code for now. The runtime environment will be supported by Microsoft for the foreseeable future, so there's no urgent need to migrate. Instead, start working on new functionality in ASP.NET: this way, you won't be held back by legacy concepts, and can use the new coolness afforded by the Framework (including stuff like ASP.NET MVC) in any way you see fit.
Of course, your new code will need to work with the existing ASP environment. Sharing session state between ASP and ASP.NET will most likely be one of your first requirements, but you'll soon identify more issues like that.
The 'right' solution for such issues will depend entirely on your current code and requirements: sometimes, you'll be able to wrap .NET code in a COM object for use by your ASP code, sometimes partial porting/migration may be the solution.
However, on average, the 'two worlds' approach should be entirely feasible, and allow you to develop exciting new features without having to worry about your legacy code.
December 2009 addition to original answer: Just came across the
ASP Classic Compiler, which is an actively maintained VBscript compiler that converts classic ASP pages into code that runs natively on ASP.NET. It has several cool features, such as the ability to use it as a ASP.NET MVC custom ViewEngine, so despite its beta status, it would definitely seem worth keeping an eye on...